After being in Lima for only one week, I found a position with Euro Idiomas in Camacho. The interview process was rather easy and no mention was made of legal documents. I assumed the school paid off the local authorities.

Congratulations. I love the City of Kings and am off there soon for a visit. Did you know anyone in-country before you arrived? Are you going to be finding your own apartment? You should post updates on the board for all to see and learn from.

That's great. It's not that hard to get a job at an institute. Pay is usually from 6 to 10 USD. English Life and Business LInks pay towards the top end.
Europ Idiomas don't pay off the authorities, lots of places hire people with tourist visas, it's just done.